On the locality of parallel transport of heat carrying electrons in the SOL
|
|
- Lauren Fowler
- 6 years ago
- Views:
Transcription
1 P1-068 On the locality of parallel transport of heat carrying electrons in the SOL A.V. Chankin* and D.P. Coster Max-Planck-Institut für Pasmaphysik, Garching, Germany Abstract A continuum Vlasov-Fokker-Planck code KIPP is used to assess the degree of locality of parallel transport of heat carrying electrons (HCE) in collisional SOLs. It is shown that for typical SOL collisionalities, the HCE are marginally collisional, justifying attempts to parameterize kinetic code results of transport parameters such as parallel heat flux and ionelectron thermoforce in the present 2D fluid codes. A kinetic solution for the case of 90% recycling at the target and factor 10 T e drop along the field line is also presented, showing the degree of heat flux limiting upstream and enhancement downstream, compared to predictions of the Braginskii s (or Spitzer-Härm s) formulas. Possible causes of these features are discussed. JNM keywords: Plasma-Materials Interaction, Plasma Properties PSI-20 keywords: kinetic, electrons, SOL, transport, collisionality PACS: Fa, Fs, Dg, Fi *Corresponding author address: Max-Planck-Institut für Plasmaphysik, Boltzmannstr. 2, Garching, Germany *Corresponding author Alex.Chankin@ipp.mpg.de Presenting author: Dr A.V. Chankin Presenting author Alex.Chankin@ipp.mpg.de
2 1. Introduction Kinetic calculations of parallel plasma transport in the scrape-off layer (SOL) and divertor may be very CPU time consuming due to the need to set the time step ( t) to a fraction of the Coulomb collision time, τ e, coll.. The latter drops to very low levels in cold and dense divertor plasmas owing to 3/2 e, coll. Te /ne τ. The requirement to adjust t to low τ e, coll. in the divertor, combined with long calculation times necessary to describe the (much slower) evolution of the upstream plasma, may prevent completion of calculations (e.g. reaching a steady state solution) in a reasonable amount of time. There is therefore a strong demand for analytical and computational efforts that would, ideally, allow parameterization of main kinetic results such as the ratio of parallel electron heat conductivity to that calculated according to Braginskii s (or Spitzer-Härm s) formulas, χ e/χ e, Brag, against plasma parameters and their spatial derivatives. This however may only be possible if super-thermal electrons carrying the bulk of the parallel heat flux (Heat Carrying Electrons, or HCE) are not collisionless, otherwise the heat transport becomes strongly non-local and only fully kinetic calculations can yield trustable results. Due to its accuracy, KIPP (KInetic Code for Plasma Periphery) [1-3] is an ideal tool to address the issue of a possible parameterization of kinetic code results. Various aspects of parallel transport of HCE, related to their collisionality, are discussed in the paper. Earlier contributions towards inclusion of non-local effects in fluid models for the parallel plasma transport, in particular the use of integral kernels for the calculation of parallel heat conduction, can be found e.g. in Ref. [4]. 2
3 2. Collision mean free path for a typical/representative heat-carrying electron (HCE) KIPP uses dimensionless parameters described in [1]: dimensionless distance along the field line ~ s = s / s, where o o voτ o s =, v o = To / me (T o some reference electron temperature), 3 o 2 4 collision time τ o = v me /(4e noλo). Distance s o is calculated upstream, at the stagnation point, where dimensionless temperature and density T ~ = n~ = 1. Hence, the spatial size of the grid in ~ s corresponds to the number of collision mean free paths (m.f.p.) calculated at the stagnation point, along parallel distance, which is an approximate measure of collisionality of the KIPP case. It has to be noted that, owing to different definitions of collision time, SOL (electron) collisionality ν SOL, defined by Stangeby ([5], p.194), is by factor 3.76 smaller than collisionality defined by using 1 /τo here, which may be referred to as ν KIPP. Below, tilde signs (~) for dimensionless parameters will often be omitted. For the study of the HCE collisionality, a strongly collisional KIPP case, as close as possible to assumptions of analytical theory of infinite collisionality, was chosen, with ~ s =1000, small ( 10%) T e drop from the stagnation point to the target, and fine velocity grid: 400 cells in v and 200 in v, with the maximum velocity v max = 7vo (see details of this case in Fig. (1) of [3]). The electron distribution function f e was selected in the middle of the spatial grid, where the heat conduction coefficient χ e was found to be very close to the Braginskii s (Eq. (2.12) of [6]). In all KIPP cases referred to here the number of spatial cells is 63, which corresponds to the number of processes used in the MPI parallelization (64) minus one processor dedicated to some common tasks including output of results. 3
4 Simple estimates of the collisionality of the HCE are based on the scaling 4 λei v e. From Chodura s calculations [7], the maximum of the parallel electron heat flux density 2 m v = f e e e ve dv is reached at v/v th = 3.74, with v th = Te /me, from where one may 2 q e conclude that the collisionality of the HCE is by factor ~ lower than that of thermal electrons, which would make HCE almost collisionless in many plasma conditions encountered in the SOL and divertor. In reality, the collisionality of the HCE is much stronger, when more refined estimates of the m.f.p. are made. Fig. 1 shows the dependence of the energy density flux on absolute electron velocity and the integral of this quantity over velocity, calculated by KIPP. The maximum of the heat flux density is reached at v/v th = 3.45, which is lower than in Chodura s calculations but is very close to the value (3.44) obtained with the kinetic code ALLA (Fig. 11 of [8]), where heat flux density was plotted vs. electron energy. The difference with the Chodura s result can be explained by the use of an approximate collision operator in [8]. Chodura concluded that most of the contribution to electron heat flux comes from electrons with energy ~ 10T e. A more precise estimate following from v/v th = gives electron kinetic energy of 3.45 Te /2 = 5.95Te for the peak in energy flux. Alternatively, one could also take the velocity corresponding to a half of the integrated energy flux (Fig. 1), v/v th = 3.75 as a characteristic HCE velocity. This would give 7.03T e for 2 the HCE energy. We will be assuming here that the ratio v/vth for the characteristic HCE is somewhere between 3.45 and
5 In order to estimate the collision m.f.p. λ ei for HCE even more precisely, one needs to know separately their characteristic v and v. Fig. 2 shows the 2D contour plot of the heat flux density q e vs. v and v obtained in the same KIPP run as the one used in Fig. 1. The peak in e reached at v =2.74v th, v =1.92 v th, corresponding to q is 5.60T e of the kinetic energy, which is < 5.95T e following from Fig. 1. In order to normalize to the latter value, a flux expansion coefficient of the contour plot Fig. 2, reflecting wider density flux distributions at higher energies (wider separation of the isocontour lines at higher v / vth and v / vth ), can be applied to the velocities, leading to slightly corrected values: v =2.82v th, v =1.98v th. Hence, 2.82 can be taken as a factor of an increase in the HCE parallel velocity compared to the thermal velocity ( v hce/ Te /m ). An increase in the collision time is approximately given by τ τ hce th 3/2 εhce 1.5T, e where ε=5.95t e. Altogether, a factor of the m.f.p. increase of the HCE compared to thermal electrons is given by λ λ 3/2 hce th e ε hce 1.5T v hce = If one used the characteristic HCE T /m e energy of 7.03T e instead of 5.95T e, one would have obtained: λ hce /λ th = One may therefore conclude that the HCE collisionality is approximately by factor 20 to 30 lower than that of thermal electrons. For cases with lower collisionalities and steeper T e profiles, maxima in qe are achieved at somewhat larger v/v th. Still, this doesn t change the conclusion that for typical SOLs with dimensionless electron collisionality for thermal electrons in the range of [5] HCE appear to be marginally collisional. One may therefore attempt to parametrise macroscopic quantities such as electron parallel heat conduction against plasma parameters and their 1 st and 2 nd derivatives. 5
6 3. KIPP case with the large T e drop Fig. 3 shows a quasi steady state solution of the KIPP case with ~ 10 times T e drop from the stagnation point to the Debye sheath (target) achieved by an artificial exponential power sink profile near the target with the spatial decay length of 1/8 th of the whole domain, with the feedback on the T e in the last cell bordering the target, aiming at maintaining it at 0.1 (in relative units). In addition, power and particle sources with the same profile were specified near the stagnation point, feedbacked on the stagnation point parameters to maintain T ~ = n~ 1, and the e e = particle source near the target with the same profile was used, adjusted to match the particle sink calculated by assuming 90% ion recycling at the target. The spatial grid was 100s o wide, with s o calculated for parameters at the stagnation point, hence, corresponding to 100 electron collision SOL m.f.p. at these parameters, or to ν 27 upstream, using Stangeby s collisionality. In order to cover wide range of T e and T e variations, slightly exponential velocity and spatial grids, with every subsequent grid size larger than the previous by factor 1.03 for both grids, were used. All other assumptions were most generic, with the ionization effect achieved by simply scaling the density of the electron distribution function f e and an automatic adjustment of T i to match T e, hence, implying unspecified ion heat sources. A simple fluid ion model (for deuterium) without parallel viscosity was used. The ion Mach number at the target reached 1.87 (the minimum Mach number was set to 1, but the maximum was not limited). In order to obtain correct transport ~ coefficients, a very small time step t = was chosen, which would translate into the time step 0.1τ o (using the local τ o ) for the much more collisional plasma in the cell adjacent to the target. 6
7 As one can see from Fig. 3, the ratio of the parallel electron heat conduction q e to that calculated according to the Braginskii s formula, or, which is the same, the ratio of parallel heat conductivities, χ e/χ e, Brag, is < 1 ( heat flux limiting ) upstream and > 1 downstream ( heat flux enhancement ), close to the target, in accordance with many earlier kinetic results (see e.g. review paper [9]). Especially pronounced is a rather wide zone of the flux limiting far away from the target. Similarly, in the same region the ratio of the parallel electric field caused by the e-i thermoforce, over the T e gradient, ee, therm/ Te, is substantially below the theoretical level for strongly collisional plasmas, For parameterization of KIPP results, various dimensionless parameters, including local plasma collisionality, and 1 st and 2 nd derivatives of T e and n e, will be tried in the future. Also, different KIPP runs, obtained by varying the recycling level, and using the ion fluid model of SOLPS (B2), as well as its fluid neutral model, are planned. One of the most important dimensionless parameters is likely to be plasma collisionality calculated by taking the parallel T e decay length, λt e = T / T, as a characteristic distance: νλ λt /vteτo. It is plotted in Fig. 3 (bottom e e T e e box). Values ~ 300 imply that HCE for this case are marginally collisional, as one has to bear in mind the factor reduction in the HCE collisionality compared to that of thermal electrons and the factor 3.76 reduction in their collisionality compared to the standard, Stangeby s, definition of dimensionless collisionality. Since χ is seen rising for s from 20 to 80, e/χ e, Brag while ν λ Te remains nearly constant, it is clear that ν λ Te along would be insufficient to parameterize the results, and the second derivative of T e will probably be required, as well as, possibly, density derivatives. 7
8 4. Influence of the stagnation point and Debye sheath In KIPP, presently the left-right symmetry of f e at the stagnation point is assumed: f e + ( v ) = fe( v ). This certainly makes an impact on the χ e/χ e, Brag ratio, since right at this point no heat flux is possible. Despite the rise in νλ Te towards the stagnation point, which should make the plasma more collisional and raise the χ ratio, it is seen falling. This indicates e/χ e, Brag that a separate parameterization may be required in the vicinity of the T e maximum. Near the target, the increase in χ may be related to the steepening of the T e profile. e/χ e, Brag Oscillations in q e/q e, Brag and ee, therm/ Te profiles in the last 3 cells adjacent to the target are not due to the effect of the Debye sheath, but rather due to numerical problems: for the parallel free-streaming scheme adopted, information on the f e at each cell face requires knowledge of f e s at 4 cells closest to it (2 from each side). This is impossible to specify for the last real cell face near the target, and a simpler scheme was used for this cell face. At the same time, the influence of the Debye sheath itself on the rise in the χ ratio at e/χ e, Brag the target is probably very limited. It is clear that the truncation of f e (v ) at the Debye sheath for high negative velocities (electrons beyond certain parallel energy impacting on the target get deposited to it, hence, no such electrons are reflected back to the plasma) automatically creates parallel electron power flux to the target. However, this effect should be small for cases with large T e drops from the stagnation point to the target. A dedicated KIPP case with the plasma flowing to the target at the ion sound speed with spatially constant n e and T e (with power 8
9 supplied into boundary cells in order to maintain spatially constant T e ) was run in order to assess how long-distant is the effect of the Debye sheath on the target heat flux created by it. The maximum in q e, reached at the target, was found to decay by factor 10 over a distance of 11.8s o (11.8 collisional m.f.p.). For the case shown in Fig. 3, taking into account a much higher plasma collisionality near the target, this would translate into the distance s = 0.51, which is close to the boundary cell size. Hence, the effect of the Debye sheath should decay very quickly. 5. Summary For typical plasma collisionalities encountered in the SOL heat carrying electrons (HCE) are in the marginal collisionality regime. This makes the problem of avoiding very CPU time consuming kinetic calculations for purposes of correctly calculating parallel heat fluxes and their replacement with parameterization formulas particularly challenging. HCE are neither enough collisional, which would have justified simple corrections to fluid results using only plasma parameters and their derivatives, nor are they enough collisionless, which would have enabled one to consider Coulomb collisions as a correction to collisionless solutions. The marginal collisionality however does not rule out devising more sophisticated parameterization formulas for deviations of transport coefficients from results of analytic theory for strongly collisional plasmas. At present, KIPP results, obtained under very simplified assumptions about plasma density evolution, can only be indicative of the need to develop rather sophisticated parameterization formulas. As a next step, coupling of the electron kinetic description of KIPP with the ion fluid model of SOLPS (B2) and its fluid neutral model is planned. This will provide more material for 9
10 the development of parameterization formulas. The sensitivity of the code results to peculiarities of electron-neutral (and in the future, electron-impurity) interaction mechanisms will also be assessed. It is hoped that, owing to the long distant nature of Coulomb collisions, the influence of electrons interaction with neutrals and impurities, apart from creating particle and power sources, will be secondary, due to much smaller cross-sections. Acknowledgement This project has received funding from the Euratom research and training programme References [1] A.V. Chankin, D.P. Coster, and G. Meisl, Contrib. Plasma Phys. 52 (2012) 500. [2] G. Meisl, A.V. Chankin, and D.P. Coster, J. Nucl. Mater. 428 (2013) S342. [3] A.V. Chankin and D.P. Coster, Benchmarks of KIPP: Vlasov-Fokker-Planck Code for Parallel Plasma Transport in the SOL and Divertor, accepted for publication in Contrib. Plasma Physics. [4] J.T. Omotani and B.D. Dudson, Plasma Phys. Control. Fusion 55 (2013) [5] P.C. Stangeby, in The Boundary of Magnetic Fusion Devices, IOP Publishing, Bristol (2000). [6] S.I.Braginskii, in Transport processes in a plasma, Review of Plasma Physics Vol. 1, A.M.Leontovich (ed.), Consultants Bureau, New York (1965). [7] R. Chodura, Contrib. Plasma Phys. 32 (1992) 3/4, 219. [8] O. V. Batishchev, S. I. Krasheninnikov, P. J. Catto et al., Phys. Plasmas 4 (1997) [9] W. Fundamenski, Plasma Phys. Control. Fusion 47 R163 (2005). 10
11 Figure captions Fig. 1. Parallel electron energy density flux vs. normalized absolute electron velocity (solid line) and its integral (dotted line) obtained in a strongly collisional KIPP case. Fig. 2. 2D contour plot of the parallel electron energy density flux against normalized parallel and perpendicular electron velocities for the same case as shown in Fig. 1. Fig. 3. Output profiles for the KIPP case with the factor 10 T e drop from the stagnation point to the target: normalized T e (top box), normalized n e (2 nd from top), ratio of parallel electron heat flux to that calculated according to the Braginskii s formula (3 rd from top), ratio of electron-ion thermoforce to n e parallel T e gradient (4 th from top), and electron collisionality calculated by taking the parallel T e decay length as a characteristic spatial scale (bottom box). 11
12 Fig. 1 Fig. 2 Fig. 3 12
ASCOT simulations of electron energy distribution at the divertor targets in an ASDEX Upgrade H-mode discharge
ASCOT simulations of electron energy distribution at the divertor targets in an ASDEX Upgrade H-mode discharge L K Aho-Mantila 1, T Kurki-Suonio 1, A V Chankin 2, D P Coster 2 and S K Sipilä 1 1 Helsinki
More informationImpact of neutral atoms on plasma turbulence in the tokamak edge region
Impact of neutral atoms on plasma turbulence in the tokamak edge region C. Wersal P. Ricci, F.D. Halpern, R. Jorge, J. Morales, P. Paruta, F. Riva Theory of Fusion Plasmas Joint Varenna-Lausanne International
More informationModelling of JT-60U Detached Divertor Plasma using SONIC code
J. Plasma Fusion Res. SERIES, Vol. 9 (2010) Modelling of JT-60U Detached Divertor Plasma using SONIC code Kazuo HOSHINO, Katsuhiro SHIMIZU, Tomonori TAKIZUKA, Nobuyuki ASAKURA and Tomohide NAKANO Japan
More informationDiscrepancy between modelled and measured radial electric fields in the scrape-off layer of divertor tokamaks: a challenge for 2D fluid codes?
Discrepancy between modelled and measured radial electric fields in the scrape-off layer of divertor tokamaks: a challenge for 2D fluid codes? A.V. Chankin 1, D.P.Coster 1, N.Asakura 2, X.Bonnin 3, G.D.Conway
More information3D analysis of impurity transport and radiation for ITER limiter start-up configurations
3D analysis of impurity transport and radiation for ITER limiter start-up configurations P2-74 X. Zha a*, F. Sardei a, Y. Feng a, M. Kobayashi b, A. Loarte c, G. Federici c a Max-Planck-Institut für Plasmaphysik,
More informationIntegrated Simulation of ELM Energy Loss Determined by Pedestal MHD and SOL Transport
1 Integrated Simulation of ELM Energy Loss Determined by Pedestal MHD and SOL Transport N. Hayashi, T. Takizuka, T. Ozeki, N. Aiba, N. Oyama Japan Atomic Energy Agency, Naka, Ibaraki-ken, 311-0193 Japan
More informationPlasma-neutrals transport modeling of the ORNL plasma-materials test stand target cell
Plasma-neutrals transport modeling of the ORNL plasma-materials test stand target cell J.M. Canik, L.W. Owen, Y.K.M. Peng, J. Rapp, R.H. Goulding Oak Ridge National Laboratory ORNL is developing a helicon-based
More informationEffect ofe B driven transport on the deposition of carbon in the outer divertor of ASDEX Upgrade
Effect ofe B driven transport on the deposition of carbon in the outer divertor of ASDEX Upgrade 0-29 L. Aho-Mantila a,b *, M. Wischmeier c, K. Krieger c, V. Rohde c, H.W. Müller c, D.P. Coster c, M. Groth
More informationEffect of ExB Driven Transport on the Deposition of Carbon in the Outer Divertor of. ASDEX Upgrade
Association Euratom-Tekes ASDEX Upgrade Effect of ExB Driven Transport on the Deposition of Carbon in the Outer Divertor of ASDEX Upgrade L. Aho-Mantila 1,2, M. Wischmeier 3, K. Krieger 3, V. Rohde 3,
More informationDIVIMP simulation of W transport in the SOL of JET H-mode plasmas
DIVIMP simulation of W transport in the SOL of JET H-mode plasmas A. Järvinen a, C. Giroud b, M. Groth a, K. Krieger c, D. Moulton d, S. Wiesen e, S. Brezinsek e and JET- EFDA contributors¹ JET-EFDA, Culham
More informationA kinetic neutral atom model for tokamak scrape-off layer tubulence simulations. Christoph Wersal, Paolo Ricci, Federico Halpern, Fabio Riva
A kinetic neutral atom model for tokamak scrape-off layer tubulence simulations Christoph Wersal, Paolo Ricci, Federico Halpern, Fabio Riva CRPP - EPFL SPS Annual Meeting 2014 02.07.2014 CRPP The tokamak
More informationNonlocal heat flux application for Scrape-off Layer plasma
Nonlocal heat flux application for Scrape-off Layer plasma Hugo Bufferand, G. Ciraolo, P Di Cintio, N Fedorczak, Ph Ghendrih, S. Lepri, R. Livi, Yannick Marandet, E. Serre, P. Tamain To cite this version:
More information14. Energy transport.
Phys780: Plasma Physics Lecture 14. Energy transport. 1 14. Energy transport. Chapman-Enskog theory. ([8], p.51-75) We derive macroscopic properties of plasma by calculating moments of the kinetic equation
More informationOn existence of resistive magnetohydrodynamic equilibria
arxiv:physics/0503077v1 [physics.plasm-ph] 9 Mar 2005 On existence of resistive magnetohydrodynamic equilibria H. Tasso, G. N. Throumoulopoulos Max-Planck-Institut für Plasmaphysik Euratom Association
More informationGA A23411 COMPARISON OF LANGMUIR PROBE AND THOMSON SCATTERING MEASUREMENTS IN DIII D
GA A23411 COMPARISON OF LANGMUIR PROBE AND THOMSON SCATTERING by J.G. WATKINS, P.C. STANGEBY, J.A. BOEDO, T.N. CARLSTROM, C.J. LASNIER, R.A. MOYER, D.L. RUDAKOV, D.G. WHYTE JULY 2000 DISCLAIMER This report
More informationTH/P4-9. T. Takizuka 1), K. Shimizu 1), N. Hayashi 1), M. Hosokawa 2), M. Yagi 3)
1 Two-dimensional Full Particle Simulation of the Flow Patterns in the Scrape-off-layer Plasma for Upper- and Lower- Null Point Divertor Configurations in Tokamaks T. Takizuka 1), K. Shimizu 1), N. Hayashi
More informationITER Divertor Plasma Modelling with Consistent Core-Edge Parameters
CT/P-7 ITER Divertor Plasma Modelling with Consistent Core-Edge Parameters A. S. Kukushkin ), H. D. Pacher ), G. W. Pacher 3), G. Janeschitz ), D. Coster 5), A. Loarte 6), D. Reiter 7) ) ITER IT, Boltzmannstr.,
More informationParallel transport and profile of boundary plasma with a low recycling wall
1 TH/P4-16 Parallel transport and profile of boundary plasma with a low recycling wall Xian-Zhu Tang 1 and Zehua Guo 1 1 Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.A.
More informationSimulation of ASDEX Upgrade Ohmic Plasmas for SOLPS Code Validation
Simulation of ASDEX Upgrade Ohmic Plasmas for SOLPS Code Validation A.V.Chankin, D.P.Coster, R.Dux, Ch.Fuchs, G.Haas, A.Herrmann, L.D.Horton, A.Kallenbach, B.Kurzan, H.W.Müller, R.Pugno, M.Wischmeier,
More informationDriving Mechanism of SOL Plasma Flow and Effects on the Divertor Performance in JT-60U
EX/D-3 Driving Mechanism of SOL Plasma Flow and Effects on the Divertor Performance in JT-6U N. Asakura ), H. Takenaga ), S. Sakurai ), G.D. Porter ), T.D. Rognlien ), M.E. Rensink ), O. Naito ), K. Shimizu
More informationPSI meeting, Aachen Germany, May 2012
Constraining the divertor heat width in ITER D.G. Whyte 1, B. LaBombard 1, J.W. Hughes 1, B. Lipschultz 1, J. Terry 1, D. Brunner 1, P.C. Stangeby 2, D. Elder 2, A.W. Leonard 3, J. Watkins 4 1 MIT Plasma
More informationImpurity Seeding in ASDEX Upgrade Tokamak Modeled by COREDIV Code
Contrib. Plasma Phys. 56, No. 6-8, 772 777 (2016) / DOI 10.1002/ctpp.201610008 Impurity Seeding in ASDEX Upgrade Tokamak Modeled by COREDIV Code K. Gała zka 1, I. Ivanova-Stanik 1, M. Bernert 2, A. Czarnecka
More informationModelling of prompt deposition of tungsten under fusion relevant conditions
EUROFUSION WPPFC-CP(16) 1532 A Kirschner et al. Modelling of prompt deposition of tungsten under fusion relevant conditions Preprint of Paper to be submitted for publication in Proceedings of 26th IAEA
More informationModeling and analysis of surface roughness effects on sputtering, reflection and sputtered particle transport *
278 Journai of Nuclear Materials 176 & 177 (1990) 278-282 North-Holland Modeling and analysis of surface roughness effects on sputtering, reflection and sputtered particle transport * J.N. Brooks Argonne
More informationHistory of PARASOL! T. Takizuka! Graduate School of Engineering, Osaka University!! PARASOL was developed at Japan Atomic Energy Agency!
History of PARASOL! T. Takizuka!!! Graduate School of Engineering, Osaka University!! PARASOL was developed at Japan Atomic Energy Agency! OSAKA UNIVERSITY! 20th NEXT Meeting, Kyoto Terrsa, Kyoto, 13-14
More informationGA A27235 EULERIAN SIMULATIONS OF NEOCLASSICAL FLOWS AND TRANSPORT IN THE TOKAMAK PLASMA EDGE AND OUTER CORE
GA A27235 EULERIAN SIMULATIONS OF NEOCLASSICAL FLOWS AND TRANSPORT IN THE TOKAMAK PLASMA EDGE AND OUTER CORE by E.A. BELLI, J.A. BOEDO, J. CANDY, R.H. COHEN, P. COLELLA, M.A. DORF, M.R. DORR, J.A. HITTINGER,
More informationA neoclassical model for toroidal rotation and the radial electric field in the edge pedestal. W. M. Stacey
A neoclassical model for toroidal rotation and the radial electric field in the edge pedestal W. M. Stacey Fusion Research Center Georgia Institute of Technology Atlanta, GA 30332, USA October, 2003 ABSTRACT
More informationMonte Carlo Collisions in Particle in Cell simulations
Monte Carlo Collisions in Particle in Cell simulations Konstantin Matyash, Ralf Schneider HGF-Junior research group COMAS : Study of effects on materials in contact with plasma, either with fusion or low-temperature
More informationGA A26119 MEASUREMENTS AND SIMULATIONS OF SCRAPE-OFF LAYER FLOWS IN THE DIII-D TOKAMAK
GA A26119 MEASUREMENTS AND SIMULATIONS OF SCRAPE-OFF LAYER FLOWS IN THE DIII-D TOKAMAK by M. GROTH, G.D. PORTER, J.A. BOEDO, N.H. BROOKS, R.C. ISLER, W.P. WEST, B.D. BRAY, M.E. FENSTERMACHER, R.J. GROEBNER,
More informationBenchmarking Tokamak Edge Modelling Codes
EFDA JET CP(7)3/1 D.P. Coster, X. Bonnin, A. Chankin, G. Corrigan, W. Fundamenski, L. Owen, T. Rognlien, S. Wiesen, R. Zagórski and JET EFDA contributors Benchmarking Tokamak Edge Modelling Codes This
More informationScaling of divertor heat flux profile widths in DIII-D
1 Scaling of divertor heat flux profile widths in DIII-D C.J. Lasnier 1, M.A. Makowski 1, J.A. Boedo 2, N.H. Brooks 3, D.N. Hill 1, A.W. Leonard 3, and J.G. Watkins 4 e-mail:lasnier@llnl.gov 1 Lawrence
More informationFigure 1.1: Ionization and Recombination
Chapter 1 Introduction 1.1 What is a Plasma? 1.1.1 An ionized gas A plasma is a gas in which an important fraction of the atoms is ionized, so that the electrons and ions are separately free. When does
More informationL-Mode and Inter-ELM Divertor Particle and Heat Flux Width Scaling on MAST
CCFE-PR(13)33 J. R. Harrison, G. M. Fishpool and A. Kirk L-Mode and Inter-ELM Divertor Particle and Heat Flux Width Scaling on MAST Enquiries about copyright and reproduction should in the first instance
More informationThis is a repository copy of Using SOLPS to confirm the importance of total flux expansion in Super-X divertors.
This is a repository copy of Using SOLPS to confirm the importance of total flux expansion in Super-X divertors. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/118941/ Version:
More informationMean-field and turbulent transport in divertor geometry Davide Galassi
Mean-field and turbulent transport in divertor geometry Davide Galassi In collaboration with: Ph. Ghendrih, P. Tamain, C. Baudoin, H. Bufferand, G. Ciraolo, C. Colin and E. Serre Our goal: quantify turbulence
More informationEstimating the plasma flow in a recombining plasma from
Paper P3-38 Estimating the plasma flow in a recombining plasma from the H α emission U. Wenzel a, M. Goto b a Max-Planck-Institut für Plasmaphysik (IPP) b National Institute for Fusion Science, Toki 509-5292,
More information12. MHD Approximation.
Phys780: Plasma Physics Lecture 12. MHD approximation. 1 12. MHD Approximation. ([3], p. 169-183) The kinetic equation for the distribution function f( v, r, t) provides the most complete and universal
More informationSimple examples of MHD equilibria
Department of Physics Seminar. grade: Nuclear engineering Simple examples of MHD equilibria Author: Ingrid Vavtar Mentor: prof. ddr. Tomaž Gyergyek Ljubljana, 017 Summary: In this seminar paper I will
More informationScaling of divertor heat flux profile widths in DIII-D
LLNL-PROC-432803 Scaling of divertor heat flux profile widths in DIII-D C. J. Lasnier, M. A Makowski, J. A. Boedo, S. L. Allen, N. H. Brooks, D. N. Hill, A. W. Leonard, J. G. Watkins, W. P. West May 20,
More informationParticle-In-Cell Simulations of a Current-Free Double Layer
Particle-In-Cell Simulations of a Current-Free Double Layer S. D. Baalrud 1, T. Lafleur, C. Charles and R. W. Boswell American Physical Society Division of Plasma Physics Meeting November 10, 2010 1Present
More informationFluid Neutral Momentum Transport Reference Problem D. P. Stotler, PPPL S. I. Krasheninnikov, UCSD
Fluid Neutral Momentum Transport Reference Problem D. P. Stotler, PPPL S. I. Krasheninnikov, UCSD 1 Summary Type of problem: kinetic or fluid neutral transport Physics or algorithm stressed: thermal force
More informationParticle Transport Measurements in the LHD Stochastic Magnetic Boundary Plasma using Mach Probes and Ion Sensitive Probe
Particle Transport Measurements in the LHD Stochastic Magnetic Boundary Plasma using Mach Probes and Ion Sensitive Probe N. Ezumi a*, K. Todoroki a, T. Kobayashi b, K. Sawada c, N. Ohno b, M. Kobayashi
More informationEUROFUSION WPJET1-PR(16) CG Albert et al.
EUROFUSION WPJET1-PR(16) 15331 CG Albert et al. Hamiltonian approach for evaluation of toroidal torque from finite amplitude non-axisymmetric perturbations of a tokamak magnetic field in resonant transport
More informationFinite-Orbit-Width Effect and the Radial Electric Field in Neoclassical Transport Phenomena
1 TH/P2-18 Finite-Orbit-Width Effect and the Radial Electric Field in Neoclassical Transport Phenomena S. Satake 1), M. Okamoto 1), N. Nakajima 1), H. Sugama 1), M. Yokoyama 1), and C. D. Beidler 2) 1)
More informationKinetic theory of ions in the magnetic presheath
Kinetic theory of ions in the magnetic presheath Alessandro Geraldini 1,2, Felix I. Parra 1,2, Fulvio Militello 2 1. Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, Oxford
More informationWaves in plasma. Denis Gialis
Waves in plasma Denis Gialis This is a short introduction on waves in a non-relativistic plasma. We will consider a plasma of electrons and protons which is fully ionized, nonrelativistic and homogeneous.
More informationstable sheath Formation in Magnetized Plasma
J. Plasma Fusion Res. SERES, Vol.4 (2001) 578-582 stable sheath Formation in Magnetized Plasma T9MTA YuKihiro*, TAKAYAMA AriMiChi, TAKAMARU HiSANOTi ANd SATO TETSUYA National nstitute.for Fusion science,
More informationCollision Processes. n n The solution is 0 exp x/ mfp
Collision Processes Collisions mediate the transfer of energy and momentum between various species in a plasma, and as we shall see later, allow a treatment of highly ionized plasma as a single conducting
More informationPlasma Astrophysics Chapter 1: Basic Concepts of Plasma. Yosuke Mizuno Institute of Astronomy National Tsing-Hua University
Plasma Astrophysics Chapter 1: Basic Concepts of Plasma Yosuke Mizuno Institute of Astronomy National Tsing-Hua University What is a Plasma? A plasma is a quasi-neutral gas consisting of positive and negative
More informationStudying the Formation of the Pre-Sheath in an Oblique Magnetic Field using a Fluid Model and PIC Simulation
J. Plasma Fusion Res. SERIES, Vol. 8 (2009) Studying the Formation of the Pre-Sheath in an Oblique Magnetic Field using a Fluid Model and PIC Simulation Jernej KOVAI 1, Tomaž Gyergyek 2,1, Milan EREK 1,3
More informationDivertor Heat Flux Reduction and Detachment in NSTX
1 EX/P4-28 Divertor Heat Flux Reduction and Detachment in NSTX V. A. Soukhanovskii 1), R. Maingi 2), R. Raman 3), R. E. Bell 4), C. Bush 2), R. Kaita 4), H. W. Kugel 4), C. J. Lasnier 1), B. P. LeBlanc
More informationGA A26123 PARTICLE, HEAT, AND SHEATH POWER TRANSMISSION FACTOR PROFILES DURING ELM SUPPRESSION EXPERIMENTS ON DIII-D
GA A26123 PARTICLE, HEAT, AND SHEATH POWER TRANSMISSION FACTOR PROFILES DURING ELM SUPPRESSION EXPERIMENTS ON DIII-D by J.G. WATKINS, T.E. EVANS, I. JOSEPH, C.J. LASNIER, R.A. MOYER, D.L. RUDAKOV, O. SCHMITZ,
More informationA theoretical study of the energy distribution function of the negative hydrogen ion H - in typical
Non equilibrium velocity distributions of H - ions in H 2 plasmas and photodetachment measurements P.Diomede 1,*, S.Longo 1,2 and M.Capitelli 1,2 1 Dipartimento di Chimica dell'università di Bari, Via
More informationSpin Stability of Aysmmetrically Charged Plasma Dust. I.H. Hutchinson. February 2004
PSFC/JA-04-3 Spin Stability of Aysmmetrically Charged Plasma Dust I.H. Hutchinson February 2004 Plasma Science and Fusion Center Massachusetts Institute of Technology Cambridge, MA 02139 USA This work
More informationDrift-Driven and Transport-Driven Plasma Flow Components in the Alcator C-Mod Boundary Layer
Drift-Driven and Transport-Driven Plasma Flow Components in the Alcator C-Mod Boundary Layer N. Smick, B. LaBombard MIT Plasma Science and Fusion Center PSI-19 San Diego, CA May 25, 2010 Boundary flows
More informationVlasov simulations of plasma-wall interactions in a magnetized and weakly collisional plasma
PHYSICS OF PLASMAS 13, 083504 2006 Vlasov simulations of plasma-wall interactions in a magnetized and weakly collisional plasma S. Devaux a Laboratoire de Physique des Milieux Ionisés et Applications,
More informationAMSC 663 Project Proposal: Upgrade to the GSP Gyrokinetic Code
AMSC 663 Project Proposal: Upgrade to the GSP Gyrokinetic Code George Wilkie (gwilkie@umd.edu) Supervisor: William Dorland (bdorland@umd.edu) October 11, 2011 Abstract Simulations of turbulent plasma in
More informationStructure formation. Yvonne Y. Y. Wong Max-Planck-Institut für Physik, München
Structure formation Yvonne Y. Y. Wong Max-Planck-Institut für Physik, München Structure formation... Random density fluctuations, grow via gravitational instability galaxies, clusters, etc. Initial perturbations
More informationTheory of collision-dominated dust voids in plasmas
PHYSICAL REVIEW E, VOLUME 63, 056609 Theory of collision-dominated dust voids in plasmas V. N. Tsytovich* General Physics Institute, Vavilova 38, Moscow 117942, Russia S. V. Vladimirov School of Physics,
More informationExperimental results and modelling of ASDEX Upgrade partial detachment
Experimental results and modelling of ASDEX Upgrade partial detachment M. Wischmeier 1 With thanks to X. Bonnin 2, P. Börner 3, A. Chankin 1, D. P. Coster 1, M. Groth 4, A. Kallenbach 1, V. Kotov 3, H.
More informationCross-Field Plasma Transport and Main Chamber Recycling in Diverted Plasmas on Alcator C-Mod
Cross-Field Plasma Transport and Main Chamber Recycling in Diverted Plasmas on Alcator C-Mod B. LaBombard, M. Umansky, R.L. Boivin, J.A. Goetz, J. Hughes, B. Lipschultz, D. Mossessian, C.S. Pitcher, J.L.Terry,
More informationPlasmas as fluids. S.M.Lea. January 2007
Plasmas as fluids S.M.Lea January 2007 So far we have considered a plasma as a set of non intereacting particles, each following its own path in the electric and magnetic fields. Now we want to consider
More informationIntegrated Simulation of ELM Energy Loss and Cycle in Improved H-mode Plasmas
1 Integrated Simulation of ELM Energy Loss and Cycle in Improved H-mode Plasmas N. Hayashi 1), T. Takizuka 1), N. Aiba 1), N. Oyama 1), T. Ozeki 1), S. Wiesen 2), V. Parail 3) 1) Japan Atomic Energy Agency,
More informationPlasma-Wall Interaction: A Multi-Scale Problem
Plasma-Wall Interaction: A Multi-Scale Problem R. Schneider 1 Max-Planck-Institut für Plasmaphysik, EURATOM Association, Teilinstitut Greifswald, Wendelsteinstr.1, D-17491 Greifswald, Germany Abstract
More informationOne dimensional hybrid Maxwell-Boltzmann model of shearth evolution
Technical collection One dimensional hybrid Maxwell-Boltzmann model of shearth evolution 27 - Conferences publications P. Sarrailh L. Garrigues G. J. M. Hagelaar J. P. Boeuf G. Sandolache S. Rowe B. Jusselin
More informationDivertor power deposition and target current asymmetries during type-i ELMs in ASDEX Upgrade and JET
Journal of Nuclear Materials 363 365 (2007) 989 993 www.elsevier.com/locate/jnucmat Divertor power deposition and target current asymmetries during type-i ELMs in ASDEX Upgrade and JET T. Eich a, *, A.
More informationChapter 1 Direct Modeling for Computational Fluid Dynamics
Chapter 1 Direct Modeling for Computational Fluid Dynamics Computational fluid dynamics (CFD) is a scientific discipline, which aims to capture fluid motion in a discretized space. The description of the
More informationLectures on basic plasma physics: Introduction
Lectures on basic plasma physics: Introduction Department of applied physics, Aalto University Compiled: January 13, 2016 Definition of a plasma Layout 1 Definition of a plasma 2 Basic plasma parameters
More informationOverview of edge modeling efforts for advanced divertor configurations in NSTX-U with magnetic perturbation fields
Overview of edge modeling efforts for advanced divertor configurations in NSTX-U with magnetic perturbation fields H. Frerichs, O. Schmitz, I. Waters, G. P. Canal, T. E. Evans, Y. Feng and V. Soukhanovskii
More informationPHYSICS OF HOT DENSE PLASMAS
Chapter 6 PHYSICS OF HOT DENSE PLASMAS 10 26 10 24 Solar Center Electron density (e/cm 3 ) 10 22 10 20 10 18 10 16 10 14 10 12 High pressure arcs Chromosphere Discharge plasmas Solar interior Nd (nω) laserproduced
More informationONION-SKIN METHOD (OSM) ANALYSIS OF DIII D EDGE MEASUREMENTS
GA A2342 ONION-SKIN METHOD (OSM) ANALYSIS OF DIII D EDGE MEASUREMENTS by P.C. STANGEBY, J.G. WATKINS, G.D. PORTER, J.D. ELDER, S. LISGO, D. REITER, W.P. WEST, and D.G. WHYTE JULY 2 DISCLAIMER This report
More informationScaling of divertor plasma effectiveness for reducing target-plate heat flux
Scaling of divertor plasma effectiveness for reducing target-plate heat flux T.D. Rognlien, I. Joseph, G.D. Porter, M.E. Rensink, M.V. Umansky, LLNL S.I. Krasheninnikov & A.Yu. Pigarov, UCSD; M. Groth,
More informationEdge Momentum Transport by Neutrals
1 TH/P3-18 Edge Momentum Transport by Neutrals J.T. Omotani 1, S.L. Newton 1,2, I. Pusztai 1 and T. Fülöp 1 1 Department of Physics, Chalmers University of Technology, 41296 Gothenburg, Sweden 2 CCFE,
More informationBlob sizes and velocities in the Alcator C-Mod scrapeoff
P1-59 Blob sizes and velocities in the Alcator C-Mod scrapeoff layer R. Kube a,b,*, O. E. Garcia a,b, B. LaBombard b, J. L. Terry b, S. J. Zweben c a Department of Physics and Technology, University of
More information1 EX/P6-5 Analysis of Pedestal Characteristics in JT-60U H-mode Plasmas Based on Monte-Carlo Neutral Transport Simulation
1 Analysis of Pedestal Characteristics in JT-60U H-mode Plasmas Based on Monte-Carlo Neutral Transport Simulation Y. Nakashima1), Y. Higashizono1), H. Kawano1), H. Takenaga2), N. Asakura2), N. Oyama2),
More informationParticle Transport and Density Gradient Scale Lengths in the Edge Pedestal
Particle Transport and Density Gradient Scale Lengths in the Edge Pedestal W. M. Stacey Fusion Research Center, Georgia Institute of Technology, Atlanta, GA, USA Email: weston.stacey@nre.gatech.edu Abstract
More informationThe physics of the heat flux narrow decay length in the TCV scrape-off layer: experiments and simulations
EUROFUSION WPMST1-CP(16) 15302 B Labit et al. The physics of the heat flux narrow decay length in the TCV scrape-off layer: experiments and simulations Preprint of Paper to be submitted for publication
More informationSensors Plasma Diagnostics
Sensors Plasma Diagnostics Ken Gentle Physics Department Kenneth Gentle RLM 12.330 k.gentle@mail.utexas.edu NRL Formulary MIT Formulary www.psfc.mit.edu/library1/catalog/ reports/2010/11rr/11rr013/11rr013_full.pdf
More informationL-mode radiative plasma edge studies for model validation in ASDEX Upgrade and JET
L-mode radiative plasma edge studies for model validation in ASDEX Upgrade and JET P1-3 L. Aho-Mantila a *, M. Bernert b, J.W. Coenen c, R. Fischer b, M. Lehnen c, C. Lowry d, S. Marsen e, K. McCormick
More informationKinetic simulation of the stationary HEMP thruster including the near field plume region
Kinetic simulation of the stationary HEMP thruster including the near field plume region IEPC-2009-110 Presented at the 31st International Electric Propulsion Conference, University of Michigan Ann Arbor,
More informationChemical Sputtering of Carbon Materials due to Combined Bombardment by Ions and Atomic Hydrogen
Chemical Sputtering of Carbon Materials due to Combined Bombardment by Ions and Atomic Hydrogen W. Jacob, C. Hopf, and M. Schlüter Max-Planck-Institut für Plasmaphysik, EURATOM Association, Boltzmannstr.
More informationComparison of SPT and HEMP thruster concepts from kinetic simulations
Comparison of SPT and HEMP thruster concepts from kinetic simulations K. Matyash, R. Schneider, A. Mutzke, O. Kalentev Max-Planck-Institut für Plasmaphysik, EURATOM Association, Greifswald, D-1749, Germany
More informationModeling of the Transport of the Plasma and Neutrals in the Divertor Layer with 1D GARMIT Code
PFC/JA-95-7 Modeling of the Transport of the Plasma and Neutrals in the Divertor Layer with 1D GARMIT Code A. S. Kukushkin*, S. I. Krasheninnikov March 1995 MIT Plasma Fusion Center Cambridge, Massachusetts
More informationBoundary Conditions for the Child Langmuir Sheath Model
IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 6, DECEMBER 2000 2207 Boundary Conditions for the Child Langmuir Sheath Model Mikhail S. Benilov Abstract A collision-free space-charge sheath formed by
More information4 Modeling of a capacitive RF discharge
4 Modeling of a capacitive discharge 4.1 PIC MCC model for capacitive discharge Capacitive radio frequency () discharges are very popular, both in laboratory research for the production of low-temperature
More informationMitigation of ELMs and Disruptions by Pellet Injection
TH/P4-5 Mitigation of ELMs and Disruptions by Pellet Injection K. Gál ), T. Fehér ), T. Fülöp ), P. T. Lang 3), H. M. Smith 4), ASDEX Upgrade Team 5) and JET-EFDA contributors 3) ) KFKI-RMKI, Association
More informationHelium-3 transport experiments in the scrape-off layer with the Alcator C-Mod omegatron ion mass spectrometer
PHYSICS OF PLASMAS VOLUME 7, NUMBER 11 NOVEMBER 2000 Helium-3 transport experiments in the scrape-off layer with the Alcator C-Mod omegatron ion mass spectrometer R. Nachtrieb a) Lutron Electronics Co.,
More informationCharacteristics of Positive Ions in the Sheath Region of Magnetized Collisional Electronegative Discharges
Plasma Science and Technology, Vol.6, No.6, Jun. 204 Characteristics of Positive Ions in the Sheath Region of Magnetized Collisional Electronegative Discharges M. M. HATAMI, A. R. NIKNAM 2 Physics Department
More informationErosion and Confinement of Tungsten in ASDEX Upgrade
ASDEX Upgrade Max-Planck-Institut für Plasmaphysik Erosion and Confinement of Tungsten in ASDEX Upgrade R. Dux, T.Pütterich, A. Janzer, and ASDEX Upgrade Team 3rd IAEA-FEC-Conference, 4.., Daejeon, Rep.
More informationVerification & Validation: application to the TORPEX basic plasma physics experiment
Verification & Validation: application to the TORPEX basic plasma physics experiment Paolo Ricci F. Avino, A. Bovet, A. Fasoli, I. Furno, S. Jolliet, F. Halpern, J. Loizu, A. Mosetto, F. Riva, C. Theiler,
More informationEdge Impurity Dynamics During an ELM Cycle in DIII D
Edge Impurity Dynamics During an ELM Cycle in by M.R. Wade 1 in collaboration with K.H. Burrell, A.W. Leonard, T.H. Osborne, P.B. Snyder, J.T. Hogan, 1 and D. Coster 3 1 Oak Ridge National Laboratory General
More informationDivertor Requirements and Performance in ITER
Divertor Requirements and Performance in ITER M. Sugihara ITER International Team 1 th International Toki Conference Dec. 11-14, 001 Contents Overview of requirement and prediction for divertor performance
More informationFundamentals of Plasma Physics
Fundamentals of Plasma Physics Definition of Plasma: A gas with an ionized fraction (n i + + e ). Depending on density, E and B fields, there can be many regimes. Collisions and the Mean Free Path (mfp)
More informationDamping of MHD waves in the solar partially ionized plasmas
Damping of MHD waves in the solar partially ionized plasmas M. L. Khodachenko Space Research Institute, Austrian Academy of Sciences, Graz, Austria MHD waves on the Sun Magnetic field plays the key role
More informationFAR SCRAPE-OFF LAYER AND NEAR WALL PLASMA STUDIES IN DIII D
GA A24724 FAR SCRAPE-OFF LAYER AND NEAR WALL PLASMA STUDIES IN DIII D by D.L. RUDAKOV, J.A. BOEDO, R.A. MOYER, N.H. BROOKS, R.P. DOERNER, T.E. EVANS, M.E. FENSTERMACHER, M. GROTH, E.M. HOLLMANN, S. KRASHENINNIKOV,
More informationRadiative type-iii ELMy H-mode in all-tungsten ASDEX Upgrade
Radiative type-iii ELMy H-mode in all-tungsten ASDEX Upgrade J. Rapp 1, A. Kallenbach 2, R. Neu 2, T. Eich 2, R. Fischer 2, A. Herrmann 2, S. Potzel 2, G.J. van Rooij 3, J.J. Zielinski 3 and ASDEX Upgrade
More informationCorrelations of ELM frequency with pedestal plasma characteristics
cpp header will be provided by the publisher Correlations of ELM frequency with pedestal plasma characteristics G. Kamberov 1 and L. Popova 2 1 Stevens Institute of Technology, Hoboken NJ, USA 2 Institute
More information1.0. T (ev) 0.5. z [m] y [m] x [m]
W7-X edge modelling with the 3D SOL fluid code BoRiS M. Borchardt, J. Riemann, R. Schneider, X. Bonnin Max-Planck-Institut für Plasmaphysik, Teilinstitut Greifswald EURATOM Association, D 17491 Greifswald,
More informationFluid equations, magnetohydrodynamics
Fluid equations, magnetohydrodynamics Multi-fluid theory Equation of state Single-fluid theory Generalised Ohm s law Magnetic tension and plasma beta Stationarity and equilibria Validity of magnetohydrodynamics
More informationEdge Plasma Energy and Particle Fluxes in Divertor Tokamaks
Edge Plasma Energy and Particle Fluxes in Divertor Tokamaks Alberto Loarte European Fusion Development Agreement Close Support Unit - Garching Alberto Loarte New Trends in Plasma Physics II Max-Planck-Institut
More information